Independent . | Definition . | Dimensionalizing . |
---|---|---|
variables . | . | Scale . |
Macroscale position | H | |
Mesoscale position | ||
t | Time | |
Dependent | ||
variables | ||
Velocity | ||
Stress tensor | ||
Strain rate tensor | ||
Vorticity tensor | ||
Stream function | ||
Volume fraction phase i | n/a | |
Phase field wave number | ||
Grain size of phase i | ||
r | Interface roughness | |
Various | Definition | Notes, equations |
factors | ||
Reference grain size | (76) | |
Twice basic state viscosity | (79) | |
Basic state strain strain rate | (80) | |
Fabric tensor | (72) | |
Gary tensor | (46) | |
Isotropic, anisotropic viscosity contrasts | (46) | |
Zener pinning factor | (73) | |
Interface area factor | ||
Parameters | Definition | Values used |
Grain coarsening number, phase i | 0.2 | |
Interface coarsening number | ||
Grain-boundary damage number, phase i | 0.2-10 | |
Interface damage number | ||
Drip buouancy number | 3 | |
Phase mixing diffusivity | ||
p | Grain coarsening exponent | 2 |
q | Interface coarsening exponent | 4 |
n | Dislocation creep stress exponent | 3 |
m | Diffusion creep grain size exponent | 3 |
Zener pinning coefficient | 0.87 |
Independent . | Definition . | Dimensionalizing . |
---|---|---|
variables . | . | Scale . |
Macroscale position | H | |
Mesoscale position | ||
t | Time | |
Dependent | ||
variables | ||
Velocity | ||
Stress tensor | ||
Strain rate tensor | ||
Vorticity tensor | ||
Stream function | ||
Volume fraction phase i | n/a | |
Phase field wave number | ||
Grain size of phase i | ||
r | Interface roughness | |
Various | Definition | Notes, equations |
factors | ||
Reference grain size | (76) | |
Twice basic state viscosity | (79) | |
Basic state strain strain rate | (80) | |
Fabric tensor | (72) | |
Gary tensor | (46) | |
Isotropic, anisotropic viscosity contrasts | (46) | |
Zener pinning factor | (73) | |
Interface area factor | ||
Parameters | Definition | Values used |
Grain coarsening number, phase i | 0.2 | |
Interface coarsening number | ||
Grain-boundary damage number, phase i | 0.2-10 | |
Interface damage number | ||
Drip buouancy number | 3 | |
Phase mixing diffusivity | ||
p | Grain coarsening exponent | 2 |
q | Interface coarsening exponent | 4 |
n | Dislocation creep stress exponent | 3 |
m | Diffusion creep grain size exponent | 3 |
Zener pinning coefficient | 0.87 |
Notes: The damage and coarsening numbers are extracted from the comparison to lab experiments by Bercovici et al. (2023), which are for lower pressure, higher temperature and much higher strain rates than in the mantle.
Independent . | Definition . | Dimensionalizing . |
---|---|---|
variables . | . | Scale . |
Macroscale position | H | |
Mesoscale position | ||
t | Time | |
Dependent | ||
variables | ||
Velocity | ||
Stress tensor | ||
Strain rate tensor | ||
Vorticity tensor | ||
Stream function | ||
Volume fraction phase i | n/a | |
Phase field wave number | ||
Grain size of phase i | ||
r | Interface roughness | |
Various | Definition | Notes, equations |
factors | ||
Reference grain size | (76) | |
Twice basic state viscosity | (79) | |
Basic state strain strain rate | (80) | |
Fabric tensor | (72) | |
Gary tensor | (46) | |
Isotropic, anisotropic viscosity contrasts | (46) | |
Zener pinning factor | (73) | |
Interface area factor | ||
Parameters | Definition | Values used |
Grain coarsening number, phase i | 0.2 | |
Interface coarsening number | ||
Grain-boundary damage number, phase i | 0.2-10 | |
Interface damage number | ||
Drip buouancy number | 3 | |
Phase mixing diffusivity | ||
p | Grain coarsening exponent | 2 |
q | Interface coarsening exponent | 4 |
n | Dislocation creep stress exponent | 3 |
m | Diffusion creep grain size exponent | 3 |
Zener pinning coefficient | 0.87 |
Independent . | Definition . | Dimensionalizing . |
---|---|---|
variables . | . | Scale . |
Macroscale position | H | |
Mesoscale position | ||
t | Time | |
Dependent | ||
variables | ||
Velocity | ||
Stress tensor | ||
Strain rate tensor | ||
Vorticity tensor | ||
Stream function | ||
Volume fraction phase i | n/a | |
Phase field wave number | ||
Grain size of phase i | ||
r | Interface roughness | |
Various | Definition | Notes, equations |
factors | ||
Reference grain size | (76) | |
Twice basic state viscosity | (79) | |
Basic state strain strain rate | (80) | |
Fabric tensor | (72) | |
Gary tensor | (46) | |
Isotropic, anisotropic viscosity contrasts | (46) | |
Zener pinning factor | (73) | |
Interface area factor | ||
Parameters | Definition | Values used |
Grain coarsening number, phase i | 0.2 | |
Interface coarsening number | ||
Grain-boundary damage number, phase i | 0.2-10 | |
Interface damage number | ||
Drip buouancy number | 3 | |
Phase mixing diffusivity | ||
p | Grain coarsening exponent | 2 |
q | Interface coarsening exponent | 4 |
n | Dislocation creep stress exponent | 3 |
m | Diffusion creep grain size exponent | 3 |
Zener pinning coefficient | 0.87 |
Notes: The damage and coarsening numbers are extracted from the comparison to lab experiments by Bercovici et al. (2023), which are for lower pressure, higher temperature and much higher strain rates than in the mantle.
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